student22 wrote:

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x is one of the numbers: 3 or 6. Is xy equal to 12 ?

(1) Either x equals 3 or y does not equal 2.


(2) Either x equals 6 or y does not equal 4.

I found this problem in a GMAT study guide. I thought the answer would be D, but according to them, it is C, and this is their reasoning:

Note: The statement "Either A or B is true" means either A is true, or B is true, or BOTH.


Is that correct? Does the GMAT treat the phrase either/or to mean either A or B or both A and B?

"Either A or B is true" will mean at least one of the statement of A and B are true. There may be a case where both the statements are true - It also satisfies "Either A or B is true"

1) X=3 y=4 and x=3,y=5 both satisfy the first statement - Insufficient to conclude anything about xy
2) x=6 y =2 and x=6 y= 4 both satisfy the second statement - Insufficient to conclude anything about xy

Combining,
given that x =3 or x=6

Case 1; x=3 First statement is satisfied; first part of second statement is not satisfied, so second part has to be satisfied
x is not equal to 4 in whch case the product xy is not equal to 12

Case 2 x=6 Second statement is satisfied; first part of first statement is not satisfied, so second part has to be satisfied
x is not equal to 2 in whch case the product xy is not equal to 12

In both cases xy is not equal to 12; sufficient

There may be a case where both the statements are true - It also satisfies "Either A or B is true"

Thanks for the reply, but this is the part I don't get. I thought that the phrase either/or means that they are mutually exclusive.

Statement 1: X = 3 --> thus Y = 2 : 3 * 2 = 6
or Y != 2 --> X = 6 : Can't equal 12

Sufficient.


Statement 2: X = 6 --> thus Y = 4 : 6 * 4 = 24
or Y!= 4 --> X = 3 : Can't equal 12

Sufficient

student22 wrote:
Thanks for the reply, but this is the part I don't get. I thought that the phrase either/or means that they are mutually exclusive.

In Either or Statements there is no requirement that exactly one part statement is true. It can happen that both part of the statements are true. It is much like the "or" gate if you are into binary logic. The phrases/parts are not mutually exclusive; to make them it should be preceded by "not both" (i.e. Either this or that, not both)

Ok, thanks for the clarification. This is one of those things that would've gotten me for sure if it came up on the GMAT.

I always thought that either/or meant it had to be one or the other.